Question: What is the value of the following logarithm? $\log_{12} \left(\dfrac{1}{144}\right)$
If $b^y = x$ , then $\log_{b} x = y$ Therefore, we want to find the value $y$ such that $12^{y} = \dfrac{1}{144}$ In this case, $12^{-2} = \dfrac{1}{144}$, so $\log_{12} \left(\dfrac{1}{144}\right) = -2$.